derivepassphrase.git

1) # SPDX-FileCopyrightText: 2024 Marco Ricci <m@the13thletter.info>
2) #
3) # SPDX-License-Identifier: MIT
4) 
5) """A Python reimplementation of James Coglan's "sequin" Node.js module.
6) 
7) James Coglan's "sequin" Node.js module provides a pseudorandom number
8) generator (using rejection sampling on a stream of input numbers) that
9) attempts to minimize the amount of information it throws away:
10) (non-degenerate) rejected samples are fed into a stream of higher-order
11) numbers from which the next random number generation request will be
12) served.  The sequin module is used in Coglan's "vault" module (a
13) deterministic, stateless password manager that recomputes passwords
14) instead of storing them), and this reimplementation is used for
15) a similar purpose.
16) 
17) The main API is the [`Sequin`] [sequin.Sequin] class, which is
18) thoroughly documented.
19) 
20) """
21) 

22) # ruff: noqa: RUF002,RUF003
23) 

24) from __future__ import annotations
25) 
26) import collections

27) from typing import TYPE_CHECKING

28) 

29) from typing_extensions import assert_type

30) 

31) if TYPE_CHECKING:
32)     from collections.abc import Iterator, Sequence
33) 

34) __all__ = ('Sequin', 'SequinExhaustedError')

35) __author__ = "Marco Ricci <m@the13thletter.info>"

36) __version__ = "0.1.1"

37) 
38) class Sequin:
39)     """Generate pseudorandom non-negative numbers in different ranges.
40) 
41)     Given a (presumed high-quality) uniformly random sequence of input
42)     bits, generate pseudorandom non-negative integers in a certain range
43)     on each call of the `generate` method.  (It is permissible to
44)     specify a different range per call to `generate`; this is the main
45)     use case.)  We use a modified version of rejection sampling, where
46)     rejected values are stored in "rejection queues" if possible, and
47)     these rejection queues re-seed the next round of rejection sampling.
48) 
49)     This is a Python reimplementation of James Coglan's [Node.js sequin
50)     module][JS_SEQUIN], as introduced in [his blog post][BLOG_POST].  It
51)     uses a [technique by Christian Lawson-Perfect][SEQUIN_TECHNIQUE].
52)     I do not know why the original module is called "sequin"; I presume
53)     it to be a pun on "sequence".
54) 
55)     [JS_SEQUIN]: https://www.npmjs.com/package/sequin
56)     [BLOG_POST]: https://blog.jcoglan.com/2012/07/16/designing-vaults-generator-algorithm/
57)     [SEQUIN_TECHNIQUE]: https://checkmyworking.com/2012/06/converting-a-stream-of-binary-digits-to-a-stream-of-base-n-digits/
58) 
59)     """
60)     def __init__(
61)         self,
62)         sequence: str | bytes | bytearray | Sequence[int],

63)         /, *, is_bitstring: bool = False

64)     ):
65)         """Initialize the Sequin.
66) 
67)         Args:
68)             sequence:
69)                 A sequence of bits, or things convertible to bits, to
70)                 seed the pseudorandom number generator.  Byte and text
71)                 strings are converted to 8-bit integer sequences.
72)                 (Conversion will fail if the text string contains
73)                 non-ISO-8859-1 characters.)  The numbers are then
74)                 converted to bits.

75)             is_bitstring:
76)                 If true, treat the input as a bitstring.  By default,
77)                 the input is treated as a string of 8-bit integers, from
78)                 which the individual bits must still be extracted.
79) 
80)         Raises:
81)             ValueError:
82)                 The sequence contains values outside the permissible
83)                 range.

84) 
85)         """

86)         msg = 'sequence item out of range'

87)         def uint8_to_bits(value):
88)             """Yield individual bits of an 8-bit number, MSB first."""
89)             for i in (0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01):
90)                 yield 1 if value | i == value else 0
91)         if isinstance(sequence, str):

92)             try:
93)                 sequence = tuple(sequence.encode('iso-8859-1'))
94)             except UnicodeError as e:

95)                 raise ValueError(msg) from e

96)         else:
97)             sequence = tuple(sequence)
98)         assert_type(sequence, tuple[int, ...])

99)         self.bases: dict[int, collections.deque[int]] = {}
100)         def gen() -> Iterator[int]:
101)             for num in sequence:
102)                 if num not in range(2 if is_bitstring else 256):

103)                     raise ValueError(msg)

104)                 if is_bitstring:
105)                     yield num
106)                 else:
107)                     yield from uint8_to_bits(num)
108)         self.bases[2] = collections.deque(gen())

109) 
110)     def _all_or_nothing_shift(
111)         self, count: int, /, *, base: int = 2
112)     ) -> Sequence[int]:
113)         """Shift and return items if and only if there are enough.
114) 
115)         Args:
116)             count: Number of items to shift/consume.
117)             base: Use the base `base` sequence.
118) 
119)         Returns:
120)             If there are sufficient items in the sequence left, then
121)             consume them from the sequence and return them.  Otherwise,
122)             consume nothing, and return nothing.
123) 
124)         Notes:
125)             We currently remove now-empty sequences from the registry of
126)             sequences.
127) 
128)         Examples:

129)             >>> seq = Sequin([1, 0, 1, 0, 0, 1, 0, 0, 0, 1],
130)             ...              is_bitstring=True)

131)             >>> seq.bases
132)             {2: deque([1, 0, 1, 0, 0, 1, 0, 0, 0, 1])}
133)             >>> seq._all_or_nothing_shift(3)
134)             (1, 0, 1)
135)             >>> seq._all_or_nothing_shift(3)
136)             (0, 0, 1)
137)             >>> seq.bases[2]
138)             deque([0, 0, 0, 1])
139)             >>> seq._all_or_nothing_shift(5)
140)             ()
141)             >>> seq.bases[2]
142)             deque([0, 0, 0, 1])
143)             >>> seq._all_or_nothing_shift(4)
144)             (0, 0, 0, 1)
145)             >>> 2 in seq.bases  # now-empty sequences are removed
146)             False
147) 
148)         """
149)         try:
150)             seq = self.bases[base]
151)         except KeyError:
152)             return ()

153)         stash: collections.deque[int] = collections.deque()
154)         try:

155)             for _ in range(count):

156)                 stash.append(seq.popleft())
157)         except IndexError:
158)             seq.extendleft(reversed(stash))

159)             return ()

160)         # Clean up queues.
161)         if not seq:
162)             del self.bases[base]
163)         return tuple(stash)

164) 
165)     @staticmethod
166)     def _big_endian_number(
167)         digits: Sequence[int], /, *, base: int = 2
168)     ) -> int:
169)         """Evaluate the given integer sequence as a big endian number.
170) 
171)         Args:
172)             digits: A sequence of integers to evaluate.
173)             base: The number base to evaluate those integers in.
174) 
175)         Raises:
176)             ValueError: `base` is an invalid base.
177)             ValueError: Not all integers are valid base `base` digits.
178) 
179)         Examples:
180)             >>> Sequin._big_endian_number([1, 2, 3, 4, 5, 6, 7, 8], base=10)
181)             12345678

182)             >>> Sequin._big_endian_number([1, 2, 3, 4, 5, 6, 7, 8], base=100)
183)             102030405060708

184)             >>> Sequin._big_endian_number([0, 0, 0, 0, 1, 4, 9, 7], base=10)
185)             1497
186)             >>> Sequin._big_endian_number([1, 0, 0, 1, 0, 0, 0, 0], base=2)
187)             144
188)             >>> Sequin._big_endian_number([1, 7, 5, 5], base=8) == 0o1755
189)             True
190) 
191)         """

192)         if base < 2:  # noqa: PLR2004
193)             msg = f'invalid base: {base!r}'
194)             raise ValueError(msg)

195)         ret = 0
196)         allowed_range = range(base)
197)         n = len(digits)
198)         for i in range(n):
199)             i2 = (n - 1) - i
200)             x = digits[i]
201)             if not isinstance(x, int):

202)                 msg = f'not an integer: {x!r}'
203)                 raise TypeError(msg)

204)             if x not in allowed_range:

205)                 msg = f'invalid base {base!r} digit: {x!r}'
206)                 raise ValueError(msg)

207)             ret += (base ** i2) * x
208)         return ret
209) 
210)     def generate(self, n: int, /) -> int:
211)         """Generate a base `n` non-negative integer.
212) 
213)         We attempt to generate a value using rejection sampling.  If the
214)         generated sample is outside the desired range (i.e., is
215)         rejected), then attempt to reuse the sample by seeding
216)         a "higher-order" input sequence of uniformly random numbers (for
217)         a different base).
218) 
219)         Args:
220)             n:
221)                 Generate numbers in the range 0, ..., `n` - 1.

222)                 (Inclusive.)  Must be larger than 0.

223) 
224)         Returns:
225)             A pseudorandom number in the range 0, ..., `n` - 1.
226) 
227)         Raises:

228)             ValueError:
229)                 The range is empty.

230)             SequinExhaustedError:

231)                 The sequin is exhausted.
232) 

233)         Examples:
234)             >>> seq = Sequin([1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
235)             ...              is_bitstring=True)
236)             >>> seq2 = Sequin([1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
237)             ...               is_bitstring=True)
238)             >>> seq.generate(5)
239)             3
240)             >>> seq.generate(5)
241)             3
242)             >>> seq.generate(5)
243)             1
244)             >>> seq.generate(5)    # doctest: +IGNORE_EXCEPTION_DETAIL
245)             Traceback (most recent call last):
246)                 ...

247)             SequinExhaustedError: Sequin is exhausted

248) 
249)             Using `n = 1` does not actually consume input bits:
250) 
251)             >>> seq2.generate(1)
252)             0
253) 
254)             But it still won't work on exhausted sequins:
255) 
256)             >>> seq.generate(1)    # doctest: +IGNORE_EXCEPTION_DETAIL
257)             Traceback (most recent call last):
258)                 ...

259)             SequinExhaustedError: Sequin is exhausted

260) 

261)         """

262)         if 2 not in self.bases:  # noqa: PLR2004
263)             raise SequinExhaustedError

264)         value = self._generate_inner(n, base=2)
265)         if value == n:

266)             raise SequinExhaustedError

267)         return value
268) 
269)     def _generate_inner(
270)         self, n: int, /, *, base: int = 2
271)     ) -> int:
272)         """Recursive call to generate a base `n` non-negative integer.
273) 
274)         We first determine the correct exponent `k` to generate base `n`
275)         numbers from a stream of base `base` numbers, then attempt to
276)         take `k` numbers from the base `base` sequence (or bail if not
277)         possible).  If the resulting number `v` is out of range for
278)         base `n`, then push `v - n` onto the rejection queue for
279)         base `r` = `base` ** `k` - `n`, and attempt to generate the
280)         requested base `n` integer from the sequence of base `r` numbers
281)         next.  (This recursion is not attempted if `r` = 1.)  Otherwise,
282)         return the number.
283) 
284)         Args:
285)             n:
286)                 Generate numbers in the range 0, ..., `n` - 1.

287)                 (Inclusive.)  Must be larger than 0.

288)             base:
289)                 Use the base `base` sequence as a source for
290)                 pseudorandom numbers.
291) 
292)         Returns:
293)             A pseudorandom number in the range 0, ..., `n` - 1 if
294)             possible, or `n` if the stream is exhausted.
295) 

296)         Raises:
297)             ValueError:
298)                 The range is empty.
299) 

300)         Examples:
301)             >>> seq = Sequin([1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
302)             ...              is_bitstring=True)
303)             >>> seq2 = Sequin([1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
304)             ...               is_bitstring=True)
305)             >>> seq._generate_inner(5)
306)             3
307)             >>> seq._generate_inner(5)
308)             3
309)             >>> seq._generate_inner(5)
310)             1
311)             >>> seq._generate_inner(5)  # error condition: sequin exhausted
312)             5
313) 
314)             Using `n = 1` does not actually consume input bits, and
315)             always works, regardless of sequin exhaustion:
316) 
317)             >>> seq2._generate_inner(1)
318)             0
319)             >>> seq._generate_inner(1)
320)             0
321) 
322)             Using an unsuitable range will raise:
323) 
324)             >>> seq2._generate_inner(0)    # doctest: +IGNORE_EXCEPTION_DETAIL
325)             Traceback (most recent call last):
326)                 ...
327)             ValueError: invalid target range
328) 

329)         """

330)         if n < 1:

331)             msg = 'invalid target range'
332)             raise ValueError(msg)
333)         if base < 2:  # noqa: PLR2004
334)             msg = f'invalid base: {base!r}'
335)             raise ValueError(msg)

336)         # p = base ** k, where k is the smallest integer such that
337)         # p >= n.  We determine p and k inductively.
338)         p = 1
339)         k = 0
340)         while p < n:
341)             p *= base
342)             k += 1
343)         # The remainder r of p and n is used as the base for rejection
344)         # queue.
345)         r = p - n
346)         # The generated number v is initialized to n because of the
347)         # while loop below.
348)         v = n
349)         while v > n - 1:
350)             list_slice = self._all_or_nothing_shift(k, base=base)
351)             if not list_slice:

352)                 if n != 1:
353)                     return n

354)                 v = 0

355)             v = self._big_endian_number(list_slice, base=base)
356)             if v > n - 1:
357)                 # If r is 0, then p == n, so v < n, or rather
358)                 # v <= n - 1.
359)                 assert r > 0
360)                 if r == 1:
361)                     continue
362)                 self._stash(v - n, base=r)
363)                 v = self._generate_inner(n, base=r)
364)         return v
365) 
366)     def _stash(self, value: int, /, *, base: int = 2) -> None:
367)         """Stash `value` on the base `base` sequence."""
368)         if base not in self.bases:
369)             self.bases[base] = collections.deque()
370)         self.bases[base].append(value)
371) 

372) class SequinExhaustedError(Exception):

373)     """The sequin is exhausted.
374) 
375)     No more values can be generated from this sequin.
376) 
377)     """